Download Geometry Mrs. Crocker Spring 2014 Final Exam Review

Name: _________________
Mod: ____
Geometry
Mrs. Crocker
Spring 2014
Final Exam Review
Use this exam review to complete your “flip book” and to study for your upcoming exam.
You must bring with you to the exam:
1. Pencil, eraser, and calculator
2. Flip Book
1.
You may bring with you to the exam:
A handwritten 3x5 notecard with important formulas (both sides may be used)
2. This exam review (at least 50% complete) for extra credit on the exam
Your exam will consist of two parts: Multiple Choice and Free Response covering the following
chapters
Chapter 6: Polygons and Quadrilaterals
Chapter 7: Similarity
Chapter 8: Trigonometry and Right Triangles
Chapter 9: Transformations
Chapter 10: Area
Chapter 11: Surface Area and Volume
Chapter 12: Circles
Mod 5-6: Tuesday 6/3 9:35 - 11:35
Mod 14-15: Monday 6/2 12:25 - 2:25
Chapter 6 - Polygons & Quadrilaterals
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
A.
B.
C.
D.
E.
F.
Angle-Sum Theorem
Exterior Angle-Sum Theorem
Properties of Parallelograms
Rhombus, Rectangle, Square
Trapezoid & Kite
Midsegment of Trapezoid
Solve the following problems to practice these above concepts. Use a pencil and show work.
1.
What is the sum of the angle
measures of a hexagon?
2.
What is the sum of the angle
measures of an 18-gon?
For #3 & 4, find the measure of one interior angle of the following regular polygons:
3.
72-gon
4.
Pentagon
For #5 & 6, find the measure of one exterior angle of the following regular polygons:
5.
36-gon
6.
Octagon
For #7 & 8, find the value of x.
7.
8.
List the five properties of parallelograms (notes 6.2):
9.
_______________________________________________________________________________________
10.
_______________________________________________________________________________________
11.
_______________________________________________________________________________________
12.
_______________________________________________________________________________________
13.
_______________________________________________________________________________________
For #14 & 15, use the properties of parallelograms to find the value of the variable(s).
14.
15.
For #16 & 17, what values of x make each figure the given special parallelogram?
16. rhombus
17. Rectangle
For #20 – 22, decide whether the parallelogram is a rhombus, rectangle, or square. Explain.
18.
19.
20.
For #22 & 23, find x given the midsegment of the trapezoid.
22.
Find the values of the variables of the kite:
24.
23.
21.
Chapter 7 - Similarity
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
G.
H.
I.
J.
Similar Polygons
Proving Triangles are Similar
Similarity in Right Triangles
Proportions in Triangles
Solve the following problems to practice these above concepts. Use a pencil and show work.
25.
Two angles are complementary and in the ratio 1 : 4. What are the degree measures of
each of the angles?
26.
The measures of the angles of a triangle are in the extended ratio 4 : 6 : 10. What are the
measures of each of the angles?
Determine whether the triangles are similar. If so, write a similarity statement and name the
postulate or theorem you used. If not, explain.
27.
29.
28.
Find the value of z. Give the scale factor of the polygons.
For #30 – 35, use the diagram at the right,
30.
The scale factor of
31.
32.
33.
34.
35.
For #36 – 39, solve for
36.
. Find each of the following.
and .
37.
38.
39.
40.
41.
For #42 & 43, find the geometric mean for each pair of numbers.
42.
43.
Chapter 8 - Trigonometry & Right Triangles
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
K. Converse of the Pythagorean Theorem
L.
and
Triangles
M. Trig Functions
N. Angles of Depression and Elevation
Solve the following problems to practice these above concepts. Use a pencil and show work.
For #44 – 46, the lengths of the sides of a triangle are given. Classify the triangle as acute, right, or
obtuse. Show work.
44.
15, 8, 17
45.
4, 9, 11
46.
5, 6, 7
For #47 & 48, find the value of each variable:
47.
y = ________
48.
For #49 – 56, find the value of each variable.
49.
50.
51.
52.
53.
54.
x = ________
55.
56.
For #57 – 60, describe each angle (elevation or depression) as it relates to the situation in the
diagram.
27.
28.
29.
60.
61. An eagle perched 40 ft up in a tree looks down at a
angle and spots a vole. How far is
the vole from the eagle to the nearest tenth of a foot? Draw and label a diagram.
62. A person is standing 40 ft from a flagpole and can see the top of the pole at a
angle of
elevation. The person’s eye level is 4 ft from the ground. What is the height of the flagpole to the
nearest foot? Draw and label a diagram.
Chapter 9 - Transformations
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
O. Transformations
Solve the following problems to practice these above concepts. Use a pencil and show work.
63. Define an isometry: _______________________________________________________________________
For #64 & 65, graph the image of each figure under the given translation.
64.
(
)
(
)
65.
(
)
(
)
For $66 & 67, the dashed-line figure is a translation image of the solid-line figure. Write a rule to
describe each translation.
66.
67.
Each point is reflected across the line indicated. Find the coordinates of each image.
68. A across the y-axis: ____________
69. B across the x-axis: ____________
70. C across y = -1: ____________
71. D across x = -1: ____________
72. E across x = -3: ____________
For #73 & 74, given points M(-1, 3), N(2, -2), and O(3, 1), graph
and its reflection image
across the line and apply a dilation with center (0,0) and scale factor 2.
73. x = 2
74.
Dilate with scale factor of 2
For #75 – 78, tell what type(s) of symmetry each figure has. It if has line symmetry, sketch the
line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation.
75.
76.
77.
Regular
Pentagon
78.
Regular
Hexagon
The dashed-line figure is a dilation image of the solid-line figure. The labeled point is the center.
Tell whether the dilation is an enlargement or a reuction. Then find the scale factor.
79.
80.
Chapter 10 - Area
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
P.
Q.
R.
S.
T.
Area of Parallelograms & Triangles
Area of Trapezoids
Area of Rhombuses & Kites
Area of Regular Polygons
Perimeter & Area of Similar Figures
Solve the following problems to practice these above concepts. Use a pencil and show work.
For #81 – 88, find the area of each figure. Round to the nearest tenth if necessary.
81.
82.
83.
84.
85.
86.
87.
88.
For #89 & 90, find the area of each composite shape.
89.
90.
For #91 & 92, find the measure of each numbered angle:
91.
92.
For #93 & 94, the figures in each pair are similar. What are the ratio of the perimeters and the ratio
of the areas?
93.
94.
95. The areas of two similar triangles are 25 m 2 and 49 m2. Find their scale factor.
Chapter 11 - Surface Area & Volume
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
U.
V.
W.
X.
Y.
Surface Area of Prisms & Cylinders
Surface Area of Pyramids & Cones
Volume of Prisms & Cylinders
Volume of Pyramids & Cones
Spheres
Solve the following problems to practice these above concepts. Use a pencil and show work.
For #96 – 101, find the surface area of each. Round to the nearest tenth if necessary.
96.
97.
98.
99.
100.
101.
For #102 – 107, find the volume of each. Round to the nearest tenth if necessary.
102.
103.
104.
105.
106.
107.
For #108 & 109, find the surface area and volume of each sphere. Leave answers in terms of .
108.
109.
Find the surface area and volume of the composite shape. Leave answers in terms fo .
110.
Chapter 12 - Circles (also 10.6 & 10.7)
In your flip books complete the following topics. Write necessary formulas,
draw diagrams:
Z.
AA.
BB.
CC.
DD.
information, and
Arc Length
Area of Sector
Tangent Lines
Chords & Arcs
Inscribed Angles
Solve the following problems to practice these above concepts. Use a pencil and show work.
111. Name a minor arc: __________
112. Name a major arc: __________
113. Name a semicircle: __________
Find the measure of each arc in
.
114.
̂ : _______
115.
̂ : _______
116.
̂ : _______
117.
̂ : _______
118.
̂ : _______
119.
̂ : _______
For #120 & 121, find the length of the darkened arc. Round answer to the nearest tenth.
120.
121.
For #122 – 125, find the area of the shaded region. Round answers to the nearest tenth.
122.
123.
124.
125.
For #126 – 133, all lines that appear tangent are tangent. Find the value of the variable(s).
126.
127.
128.
129.
130.
131.
132.
133.
Determine whether a tangent line is shown.
132.